Comment on "Minimum Uncertainty and Entanglement"

TL;DR

This paper refutes a conjecture claiming the Heisenberg-Robertson uncertainty bound cannot be achieved in mixed states, demonstrating that the bound can indeed be reached.

Contribution

It provides a counterexample to the conjecture, showing the lower bound in the uncertainty relation can be attained in mixed states.

Findings

The conjecture is false; the bound can be reached in mixed states.

Counterexamples demonstrate the attainability of the lower bound.

Clarifies the conditions under which the uncertainty bound is saturated.

Abstract

Dass, Qureshi, and Sheel conjecture that the lower bound in the Heisenberg-Robertson uncertainty relation cannot be reached in mixed states. The conjecture is wrong.